Question

Find the inverse of each function. Is the inverse a function? f(x)=x⁷

Answer 1

The inverse of the function x^7 is x^-7 and it is also a function.

An inverse function or an anti function is defined as a function, which can reverse into another function.

A standard method to find inverse of a function is to set y=f(x)

let y= f(x)=x^7

thus

$\sqrt[7]{y}$=x

thus $f^{-1}$(y)=$\sqrt[7]{y}$

thus $f^{-1} (x)=\sqrt[7]{x}$

(To verify this if a function is inverse or not we are required to check for the identity)

f($f^{-1}$(x))=$f^{-1}$(f(x))=x

Therefore, The inverse of the function x^7 is x^-7 and it is also a function.

For further reference:

brainly.com/question/2541698?referrer=searchResults

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